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SUMMARY:An approach to the four colour theorem via Donaldson- Floer theory
  - Tomasz Mrowka (Massachusetts Institute of Technology)
DTSTART:20170816T110000Z
DTEND:20170816T120000Z
UID:TALK75811@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>This talk will outline an approach to the four colour th
 eorem using a variant of Donaldson-Floer theory.<br><br> To each trivalent
  graph embedded in 3-space\, we associate an instanton homology group\, wh
 ich is a finite-dimensional Z/2 vector space. Versions of this instanton h
 omology can be constructed based on either SO(3) or SU(3) representations 
 of the fundamental group of the graph complement.&nbsp\; For the SO(3) ins
 tanton homology there is a non-vanishing theorem\, proved using techniques
  from 3-dimensional topology: if the graph is bridgeless\, its instanton h
 omology is non-zero. It is not unreasonable to conjecture that\, if the gr
 aph lies in the plane\, the Z/2 dimension of the SO(3) homology is also eq
 ual to the number of Tait colourings which would imply the four colour the
 orem.</span>  &nbsp\;  This is joint work with Peter Kronheimer.
LOCATION:Seminar Room 1\, Newton Institute
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